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Definition: Planar Graph

Let \(G(V,E,\gamma)\) be an undirected graph \(G\) is called planar, if there exists a planar drawing for this graph.

Notes

• Please note that planarity and not a property dependent on whether the graph has loops or multiedges.
• Also, it does not matter if the edges are directed or undirected.
• Thus, for convenience reasons, we may restrict our attention to simple undirected graphs only, when we study planar graphs.

Example:

A planar graph (left) with its planar embedding (right):

A graph, which is not planar:

Mentioned in:

Chapters: 1 2
Corollaries: 3 4
Definitions: 5 6
Explanations: 7
Lemmas: 8 9
Persons: 10
Problems: 11 12
Proofs: 13 14 15 16 17 18 19 20 21 22
Propositions: 23 24 25 26 27
Solutions: 28 29
Theorems: 30 31 32 33 34 35 36 37

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References

Bibliography

1. Diestel, Reinhard: "Graph Theory, 3rd Edition", Springer, 2005